Question

1. A college admissions director wishes to estimate the mean age of all students currently enrolled. In a random sample of 81 students, the mean age is found to be 20.51 years. From past studies, the standard deviation of the population is known to be 2 years, and the population is normally distributed. Construct a 99% confidence interval of the population mean age. (10 p)

(Round off final answers to two decimal places, if appropriate. Do not round off numbers taken directly from tables).

2. You randomly select 16 cars of the same model that were sold at a car dealership and determine the number of days each car sat on the dealership’s lot before it was sold. The sample mean is 9.15 days, with a sample standard deviation of 1.6 days. Construct a 95% confidence interval for the population mean number of days the car model sits on the dealership’s lot. (10 p)

(Round off final answers to two decimal places, if appropriate. Do not round off numbers taken directly from tables).

3. A researcher collected data from a random sample of 25 high school freshmen and found the mean of the sample to be 85.40 on the Test of Critical Thinking (TCT). She also calculated the standard deviation from the sample and discovered the value was 12.30. The average score on the Test of Critical Thinking for all high school seniors in a large school district is 90.00. The researcher wants to know if the mean TCT of the 25 high school freshmen in the random sample is different from the population’s (i.e., highschool seniors) TCT mean.

(Round off final answers to two decimal places, if appropriate. Do not round off numbers taken directly from tables).

1. Write out the null and alternative hypothesis associated with the research question. (4p)

2. What type of statistical test will you use to answer the proposed research question? Is this a z-test or a t-test? (4p)

Answer 1